On the distribution of αp+β modulo one for primes of type p=ar²+1

2024/04/01 by Tatyana Todorova, Todorova, T.
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.01047

openalex publication_date 2024/04/01 · openalex created_date 2024/04/03 · openalex updated_date 2026/07/28

Abstract

A classical problem in analytic number theory is to study the distribution of fractional part αp+β modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p=ar²+1 and prove that its distribution has a similar property.

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